Geometric Function Theory: Explorations in Complex Analysis


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Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research Methodically designed with individual chapters containing a rich collection of exercises, examples, and Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren. Design and analysis of adaptive jet engine frame and thrust mounts.

Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy Riemann equations, and the corona problem.

The author adroitly weaves these varied topics to reveal a number of delightful interactions.

Complex analysis : the geometric viewpoint in SearchWorks catalog

Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index.

Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis and also to spark the interest of seasoned workers in the field the book imparts a solid education both in complex analysis and in how modern mathematics works.

Geometric Function Theory

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis -and also to spark the interest of seasoned workers in the field - the book imparts a solid education both in complex analysis and in how modern mathematics works. Krantz Steven Krantz, Ph. An award-winning teacher and author, Dr.

Complex Analysis-Analytic Function(Lecture2)

Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates.


  • Complex analysis: The geometric viewpoint.
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The second part includes various more specialized topics as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics selected include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces.

The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The author has published a number of research articles and several books on functional analysis and analytic function theory. The Schwarz Lemma and Hyperbolic Geometry. Analytic Functions.


  • Explorations in Complex Analysis | Mathematical Association of America.
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Line Integrals and Harmonic Functions. Complex Integration and Analyticity. Laurent Series and Isolated Singularities.

The Residue Calculus. The Logarithmic Integral. Harmonic Functions and the Reflection Principle.

Geometric Function Theory: Explorations in Complex Analysis Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis Geometric Function Theory: Explorations in Complex Analysis
Geometric Function Theory: Explorations in Complex Analysis Geometric Function Theory: Explorations in Complex Analysis

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